#### Transcript File

```Bill’s father is building a ramp to reach
the front porch of their house. The
ramp will rise from the flat ground to
the top of the porch. The porch is 2 feet
tall. The ramp will rise at a 10 degree
angle from the ground. How long does
the ramp need to be?
Use the steps you made last class
period to set up the problem.
The Trigonometric Functions
we will be looking at
SINE
COSINE
TANGENT
The Trigonometric Functions
SINE
COSINE
TANGENT
SINE
Prounounced
“sign”
COSINE
Prounounced
“co-sign”
TANGENT
Pronounced
“tan-gent”
Greek Letter q
Prounounced
“theta”
Represents an unknown angle
Hypotenuse (hyp)
q
q
Opposite or across from
the right angle
Opposite (opp)
q
Across from the angle
q
Not touching the angle
q
Touching the angle
q
…and not the hypotenuse
Opp
Sin 
Hyp
hypotenuse
Cos 
Hyp
Opp
Tan 
q
opposite
opposite
*
Some
Old
Hippie
Came
A
Hoppin’
Through
Our
Old Hippie Apartment
SOHCAHTOA
Old Hippie
Sin
Opp
Hyp
Cos
Hyp
Tan
Opp
*
SOHCAHTOA
Opp
Sinq
Hyp
Cosq 
Hyp
a
c
c
a
b
c
q
Opp
Tanq 
a
b
b
SOHCAHTOA
Opp
Sinq
Hyp
Cosq 
Hyp
5
7
7
5
4
7
q
Opp
Tanq 
5
4
4
SOHCAHTOA
Opp
Sinq
Hyp
Cosq 
Hyp
8
12
12
8
7
12
q
Opp
Tanq 
8
7
7
Find the sine, the cosine, and the tangent of angle A.
Give a fraction and decimal answer (round to 4 places).
10.8
9
A
9
opp

sin A 
hypo 10.8  .8333
6
cos A 

hypo 10.8
 .5555
6
opp
tan A 
9

6
 1.5
Find the sine, the cosine, and the tangent of angle A
B
Give a fraction and
to 4 decimal places).
24.5
8.2
A
23.1
opp  8.2
sin A 
 .3347
24
.
5
hypo
23.1

cos A 
24.5  .9429
hypo
opp
tan A 
8 .2

23.1  .3550
*
12
X
52
*
X
36
25
Ex.
A surveyor is standing 50 feet from the base of a
large tree. The surveyor measures the angle of
elevation to the top of the tree as 71.5°. How tall
is the tree?
tan
71.5°
?
50
71.5
°
Opp

Hyp
y

50
tan
71.5°
y = 50 (tan 71.5°)
y = 50 (2.98868)
y  149.4 ft
```